The present invention relates to a distributed arithmetic oversampling recursive digital filter. In general terms, it is used in the processing of signals and more particularly in telecommunications.
In coding-decoding-filtering systems of the PCM type (pulse code modulation) operating by interpolative coding and digital filtering, undersampling and oversampling digital filters are used. These are filters for which the sampling frequency of the input signals f.sub.E and that of the output signals f.sub.S are not identical. For undersampling we obtain f.sub.E &gt;f.sub.S and for oversampling f.sub.E &lt;f.sub.S.
FIG. 1 shows the organization of such systems. They comprise a coding chain and a decoding chain. The coding chain is constituted by an analog input EA, an RC type filter 1, a double integration delta-sigma coder 2 operating for example at 2048 kHz and supplying one-bit signals at 2048 kHz, a triangular undersampling digital filter 3 supplying 13-bit signals at 16 kHz, and undersampling digital filter 4 supplying 13-bit signals at 8 kHz, a circuit 5 for compressing the linear law into law A, whose digital output SN supplies 8-bit signals at 8 kHz. In a symmetrical manner, the decoding chain comprises a digital input EN, a circuit 6 for extending law A towards the linear law, an oversampling digital filter 7 operating at 32 kHz and supplying 13-bit signals at 32 kHz, a double integration delta-sigma decoder 8 operating at 2048 KHz and supplying 1-bit signals at this frequency and finally an RC type filter 9, whose output SA supplies the restored analog signal. Naturally, the digital values given are only of an exemplary nature.
French Patent Application 79 18862 filed on July 20, 1979 and entitled "Analog double integration delta-sigma coder and digital double integration delta-sigma decoder" in particular describes circuits 2 and 8.
The specification applicable to such systems appears in report G712 of the CCITT, orange book, Vol. III-2, entitled "Quality characteristics of PCM channels at voice frequencies".
Recently, projects have been launched dealing with systems of this type having to comply with much stricter specifications than that of the aforementioned report G712, particularly with regard to the filters on transmission and reception. In order to satisfy the templates appropriate for said filters, it is necessary to use the recursive digital filtering procedure in which the output signals of the filter are reinjected at the input thereof.
In the article by G. D. TATTERSALL and M. J. CAREY entitled "Digital bandlimiting filters for PCM transmission systems" published in the Journal "IEEE Transactions on Communications", Vol. COM-27, No. 1, January 1979, pp. 240-1246, the realization of such recursive filters by using a method commonly called "distributed arithmetic" is proposed.
The present invention again takes up the idea of the distributed arithmetic recursive filter, but provides an improvement in that by a careful adaptation of the circuits inherent in distributed arithmetic and circuits which permit oversampling, it is possible to bring about a by no means negligible saving as regards the means used (particularly the number of input registers) whilst retaining a very considerable flexibility of use.
Recursive digital filtering is conventionally characterized by an expression of the following form: ##EQU1## in which x.sub.n-k designates the input signals of rank n-k, y.sub.n-k output signals of rank n-k reinjected at the input of the filters, a.sub.k coefficients of the non-recursive part, whose order is p, and b.sub.k coefficients of the recursive part, whose order is q, n assuming whole values and characterizing the output signal.
Expression (1) is a particular case of a more general expression expressing a weighted sum which can be expressed by: ##EQU2##
A recursive digital filter comprises p+1 inputs receiving signals x.sub.k and q inputs receiving signals y.sub.k, i.e., in all, p+q+1 inputs. It also comprises an output supplying the sequence of signals y.sub.n.
The transfer function H(z) of such a filter expressed by means of the complex variable z is: ##EQU3##
The invention relates to a special digital processing method called "distributed arithmetic". The latter is described in U.S. Pat. No. 3,777,130 granted on Dec. 4, 1973, to A. CROISIER, D. J. ESTEBAN, M. E. LEVILION and V. RISO, entitled "Digital filter for PCM encoded signals" as well as in the article by A. PELED and B. LIU entitled "A new hardware realization of digital filters" published in the Journal "IEEE Trans. on ASSP," Vol. ASSP-22, pp.456-462, December 1974. In addition, the article by C. S. BURRUS entitled "Digital filter structures described by distributed arithmetic" published in the Journal "IEEE Trans. on Circuits and Systems", Vol. CAS-24, No. 12, December 1977, pp.674-680, provides a general approach to this question and describes a number of algorithms and structures which can be used. Reference can be made to these documents for details concerning the distributed arithmetic method, which is only described briefly hereinafter in order to facilitate the understanding of the invention.